A new stabilized finite element method for the transient Navier-Stokes equations. (English) Zbl 1169.76392

Li, Jian; He, Yinnian; Chen, Zhangxin

Comput. Methods Appl. Mech. Eng. 197, No. 1-4, 22-35 (2007).

Summary: This paper is concerned with the development and analysis of a new stabilized finite element method based on two local Gauss integrations for the two-dimensional transient Navier-Stokes equations by using the lowest equal-order pair of finite elements. This new stabilized finite element method has some prominent features: parameter-free, avoiding higher-order derivatives or edge-based data structures, and stabilization being completely local at the element level. An optimal error estimate for approximate velocity and pressure is obtained by applying the technique of the Galerkin finite element method under certain regularity assumptions on the solution. Compared with other stabilized methods (using the same pair of mixed finite elements) for the two-dimensional transient Navier-Stokes equations through a series of numerical experiments, it is shown that this new stabilized method has better stability and accuracy results.

MSC:

76M10	Finite element methods applied to problems in fluid mechanics
76D05	Navier-Stokes equations for incompressible viscous fluids
65M15	Error bounds for initial value and initial-boundary value problems involving PDEs
65M60	Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs

Keywords:

Navier-Stokes equations; stabilized finite element method; inf-sup condition; local Gauss integration; error estimate; numerical experiments; stability

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